# How to Perform Regression in Excel and Interpretation of ANOVA

This article illustrates how to perform Regression Analysis in Excel using the Data Analysis tool and interpret the Anova Table obtained from the analysis. This technique is widely used in statistical modeling to estimate the impact of variables on a particular topic of interest.

## What Is Regression Analysis?

Regression Analysis is a set of methods used to create a relationship between a dependent variable and a single or multiple independent variables. The two most common forms of regression are:

Simple Linear Regression: You can perform this analysis when there is only one independent variable affecting the outcome of the dependent variable. The equation for simple linear regression can be represented as follows.

Y = Î±0 + Î±1X1 + Ïµ

Multiple Linear Regression: You can do this analysis when there are multiple independent variables affecting the outcome of the dependent variable. The equation for multiple linear regression can be represented as follows.

Y = Î±0 + Î±1X1 + Î±2X2 +….+ Î±nXn + Ïµ

## How to Perform Regression Analysis in Excel and Interpretation of ANOVA

### Part 1 – How to Perform Regression Analysis in Excel

We can perform Regression Analysis using the Data Analysis tool in Excel. If you need to activate the tool to be able to access it:

• Go to File >> Options or press ALT+F+T.
• Check the Analysis ToolPak checkbox.
• Click OK.

The Data Analysis tool will be available in the Data tab.

#### i – Simple Linear Regression

Suppose we have the dataset below. X is the independent variable that indicates the rates of interest, and Y is the dependent variable that indicates the price of homes. Let’s perform a regression analysis to see how these variables are related to each other.

Steps:

• Select Data >> Data Analysis.
• Choose Regression from the analysis toolbox.
• Click OK.

The Regression dialog box opens.

• Select the Y values including labels for Input Y Range and the X values for Input X Range.
• Check the Labels checkbox.
• Mark the radio button for Output Range.
• Enter the cell reference where you want to get the analysis results.
• Click OK.

The following results are returned in the specified location.

#### ii – Multiple Linear Regression

Now suppose we have the dataset below instead. Here the dependent Y variable represents the number of weekly riders in different cities. The independent X variables represent the price per week, the population of cities, monthly income of riders, and average parking rates per month respectively. Let’s verify how the independent variables affect the number of weekly riders by performing a regression analysis on the dataset.

Steps:

• Select Data >> Data Analysis.
• Choose Regression from the analysis toolbox as above.
• Click OK.

The Regression dialog box opens.

• Select the Y values including labels for Input Y Range and all of the X values for Input X Range.
• Check the Labels checkbox.
• Mark the radio button for Output Range.
• Enter the cell reference where you want to get the analysis results.
• Click OK.

The following result is returned in the specified location.

### Part 2 – How to Interpret ANOVA and Other Regression Analysis Results in Excel

The regression analysis output is divided into three different parts:

• Regression Statistics
• ANOVA Table
• Coefficients Table

We will briefly explain a few components from each part, as the rest do not have much importance.

Regression Statistics:

The two important values from this table are:

• Multiple R: This is called the correlation coefficient. It tells you how strong the linear relationship is between the independent and dependent variables. 1, -1, and 0 indicate a strong positive, a strong negative, and no relationship respectively.
• R Square: This is called the coefficient of determination. It tells you the percentages of the dependent variable that can be explained by the independent variable(s). A value closer to 1 indicates that a difference in the dependent variable can be explained by the difference in the independent variable(s) for most of the values.

ANOVA Table: The Significance F is of the most importance here.

• Significance F: A value below 0.05 indicates the linear relationship is statistically significant.

Coefficients Table: The coefficients from this table are used to form the linear equation to represent the relationship between the variables.

#### i – Simple Linear Regression

Observe the Regression Statistics table below.

• Multiple R = 0.62 indicates that the relationship between the variables is not that strong but not that weak either.
• R Square = 0.38 indicates that 38% of Y values can be explained by X values.

Observe the ANOVA Table below.

• Significance F = 0.01 < 0.05 indicates that the linear relationship between the variables is statistically significant.

Observe the Coefficient table below.

The regression equation can be Y = 393348.62 – 23409.45X + 41456.52.

#### ii – Multiple Linear Regression

Observe the Regression Statistics table.

• Multiple R = 0.97 indicates that the relationship is strong.
• R Square = 0.94 indicates that 94% of Y values can be explained by X values.

Observe the ANOVA Table below.

• Significance F < 0.05 indicates that the linear relationship between the variables is highly statistically significant.

Observe the Coefficient table below.

The regression equation can be Y = 100222.56 – 689.52X1 + 0.055X2 – 1.3X3 + 152.45X4 + 5406.37.

## Things to Remember

• Enable the Analysis ToolPak add-in to access the Data Analysis tool.
• For the Significance F, a value much smaller than the assumed confidence level means a stronger relationship.

## Related Articles

<< Go Back to Anova in Excel | Excel for StatisticsÂ |Â Learn Excel

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Md. Shamim Reza, a marine engineer with expertise in Excel and a fervent interest in VBA programming, sees programming as a time-saving tool for data manipulation, file handling, and internet interaction. His diverse skill set encompasses Rhino3D, Maxsurf C++, AutoCAD, Deep Neural Networks, and Machine Learning. He holds a B.Sc in Naval Architecture & Marine Engineering from BUET and has transitioned into a content developer role, generating technical content focused on Excel and VBA. Beyond his professional pursuits,... Read Full Bio

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